Energy conservation and axion back-reaction in a magnetic field

Axion clumps in an external magnetic field can emit electromagnetic radiation which causes them to decay. In the presence of a plasma, such radiation can become resonant if the clump frequency matches the plasma frequency. Typically, the decay or back-reaction of the clump is ignored in the literature when analyzing such radiation. In this paper we present a self consistent, semi-analytic approach which captures axion back-reaction using energy conservation. We find that inclusion of back-reaction changes the clump frequency over time enabling clumps with a range of different initial frequencies to become resonant at some point in their time evolution.